Complexity

A definition would be nice. So would an ordinal if not a cardinal measure. Is it clear that humans are more complex than whales? Than chimpanzees? Than termites? Than termite mounds?

Is there any trend towards greater complexity over time among living things? On the Earth as a whole? The universe as a whole? Is there any deep explanation (élan vital anyone?) or can it be accounted for by the usual suspects --- natural selection, "plenty of room at the top," chance? --- Even if we do come up with a measure of complexity, it will be very difficult to apply to the fossil record, since the soft parts are pretty well gone, and so we can't know (much) about the innards of the brain, or the immune system. (In fact, could you infer the existence of immune systems from the fossil record? This is important, since it's complex if anything is, and if we can't infer it, how do we know there weren't other things, also confined to the soft tissues, which weren't comprably complex?)

The "sciences of complexity" are very much a potpourri, and while the name has some justification --- chaotic motion seems more complicated than harmonic oscillation, for instance --- I think the fact that it is more dignified than "neat nonlinear nonsense" has not been the least reason for its success. --- That opinion wasn't exactly changed by working at the Santa Fe Institute for five years.

Robert Axelrod and Michael D. Cohen, Harnessing Complexity: Organizational Implications of a Scientific Frontier
John Tyler Bonner, The Evolution of Complexity, by Means of Natural Selection [Review]
Jack Cohen and Ian Stewart, The Collapse of Chaos [A great book, except that, as they themselves say of Dawkins, the philosophy is completely backwards, especially on reductionism and emergent properties.]
John Holland not only helped found evolutionary computation, but has written a good book on Emergence [Review: Game Rules, or, Emergence according to Holland, or, Confessions of a Creative Reductionist]
Steven Johnson, Emergence: The Connected Lives of Ants, Brains, Cities and Software [What I buy my relatives when they ask me what all the fuss is about.]
Heinz Pagels, The Dreams of Reason: The Computer and the Rise of the Sciences of Complexity [What I used to buy my relatives. Deserves to be brought back into print.]
Herbert Simon, The Sciences of the Artificial [Especially the last chapter, "The Architecture of Complexity". A large fraction of complexity research --- and an even larger fraction of the good stuff --- is variations on themes by Simon.]

Remo Badii and Antonio Politi, Complexity: Hierarchical Structures and Scaling in Physics [Review]
Nino Boccara, Modeling Complex Systems [Review]
Gary William Flake, The Computational Beauty of Nature [Review: A Garden of Bright Images]
Josef Honerkamp, Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis

John Bickle, "Understanding Neural Complexity: A Role for Reduction", Minds and Machines 11 (2001): 467--481
Terry Bossomaier and David Green (eds.), Complex Systems
The work of the computational mechanics group at Santa Fe is, IMHO, the closest anyone has got yet to a general, rigorous way of tackling complexity, and it is scandalously little-known. [That sentence was there years before I became part of the group --- and is still there years after I left.]
Joshua Epstein, "Agent-based Computational Models and Generative Social Science", Complexity vol. 4, no. 5 (1999): 41--60
Joshua Epstein and Robert Axtell, Growing Artificial Societies: Social Science from the Bottom Up
J. Doyne Farmer, Alan Lapedes, Norman Packard and Burton Wendroff (eds.), Evolution, Games, and Learning: Models for Adaptation in Machines and Nature (a.k.a. Physica D 22.)
Stephanie Forrest (ed.), Emergent Computation: Self-Organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks (a.k.a. Physica D 42)
Stuart Kauffman, The Origins of Order [Interesting, but the writing is confused. Favors intrinsic trends towards complexity, self-organization and "the edge of chaos."]
D. L. Stein, "Spin Glasses: Still Complex After All These Years?" cond-mat/0301104

CRS, "Methods and Techniques of Complex Systems Science: An Overview", chapter 1 (pp. 33--114) in Deisboeck and Kresh (eds.), Complex Systems Science in Biomedicine = nlin.AO/0307015

I have a long list, available upon request. I may add it here sometime when I'm feeling more full of venom than the present.

{1989--1993} Lectures in Complex Systems [Proceedings of the SFI summer schools; lots of valuable stuff, not listed under "recommended" because I'm not finished with all of them!]
K. J. Aström, Control of Complex Systems
Fatihcan Atay, Sarika Jalan and Jürgen Jost, "Randomness, chaos, and structure", arxiv:0711.4293
Sunny Auyang, Foundations of Complex Systems Theories: In Economics, Evolutionary Biology, and Statistical Physics
Bechtel and Richardson, Discovering Complexity
Bossomaier and Green, Patterns in the Sand
W. W. Burggren and M. G. Monticino, "Assessing Physiological Complexity", Journal of Experimental Biology 208 (2005): 3221--3232 [Reprint]
Eric J. Chaisson
- Cosmic Evolution : The Rise of Complexity in Nature [Review by Dan McShea in American Scientist; proposes defining complexity operationally as power dissipated per unit mass, according to McShea. Why this should be complexity, I don't get....]
- "Complexity: An Energetics Agenda", Complexity 9 (2004): 14--21 [PDF reprint from Chaisson's website]
S. V. Emelyanov and S. K. Korovin, Control of Complex and Uncertain Systems: New Types of Feedback
Nick Gessler, Artificial Culture: Experiments in Synthetic Anthropology
Giorgio Israel, "The Science of Complexity: Epistemological Problems and Perspectives", Science in Context 18 (2005): 479--509 [From the abstract: "The aim of the present article is to analyze the epistemological status attributed in the science of complexity to several fundamental ideas, such as those of scientific law, objectivity, and prediction. The aim is to show that the hope of superseding reductionism by means of concepts such as that of ��emergence�� is fallacious and that the science of complexity proposes forms of reductionism that are even more restrictive than the classical ones, particularly when it claims to unify in a single treatment problems that vary widely in nature such as physical, biological, and social problems." Thanks to Prof. Israel for a reprint.]
J. Stephen Lansing
- "Complex Adaptive Systems", Annual Review of Anthropology 32 (2003): 183--204
- Perfect Order: Recognizing Complexity in Bali [Blurb, ch. 1]
Tom Leinster
- "General self-similarity: an overview", math.DS/0411343
- "A general theory of self-similarity I", math.DS/0411344
- "A general theory of self-similarity II: recognition", math.DS/0411345
Simon Levin
- "Complex Adaptive Systems: Exploring the known, the unknown, and the unknowable", Bulletin of the American Mathematical Society 40 (2002): 3--19 [PDF. Survey, emphasis on evolutionary ecology]
- Fragile Dominion: Complexity and the Commons
Christian Lindgren, "Information Theory for Complex Systems" (Online lecture notes, dated Jan. 2003)
Melanie Mitchell, Complexity: A Guided Tour
Harold Morowitz, The Emergence of Everything
Harold Morowitz and Jerome L. Singer (eds.), The Mind, the Brain, and Complex Adaptive Systems
Giorgio Parisi, "Complex Systems: a Physicist's Viewpoint," cond-mat/0205297
Max Pettersson, Complexity and Evolution [mostly of interest to me because of the introduction by Joseph Needham]
J. Barkley Rosser, Jr., "On the Complexities of Complex Economic Dynamics", Journal of Economic Perspectives 13 (4) (1999): 169--192 [JSTOR link]
L. S. Schulman and B. Gaveau, "Complex systems under stochastic dynamics", cond-mat/0312711
Didier Sornette, Critical Phenomena in Natural Sciences: Chaos, Fractals, Self-Organization and Disorder: Concepts and Tools
Stein (ed.), Spin Glasses and Biology
Michael Strevens, Bigger than Chaos: Understanding Complexity through Probability
Tainter, Collapse of Complex Societies
Ulam, Analogies between Analogies [online]
Elias Zafiris
- "Complex Systems from the Perspective of Category Theory: I. Functioning of the Adjunction Concept," PITT-PHIL-SCI 1236
- "Complex Systems from the Perspective of Category Theory: II. Covering Systems and Sheaves," PITT-PHIL-SCI 1237

Notebooks

Complexity